The marks of history in a test are normally distributed with a mean of 55 and a standard deviation of 8 .
( a ) if 10.2 % of the students failed History , find the minimum marks needed to pass

Let X be the variable and let Z be the normalised variable, such that $\displaystyle Z = \frac{X-55}{8}$ at let W be the pass mark, so you know that $\displaystyle P(X<W) = 0.102 \ \rightarrow P(Z< \frac{W-55}{8}) = 0.102 $ now you must reference your stats table (or use technology) to find the Z value corresponding to 0.102 and solve for W.